Jack has a box in the shape of the cube, the inside edges of which are 4 inches long. What is the longest object he could fit inside the box (i.e., What is the diagonal of the cube) ?

Answer

To find the longest object that can fit inside a cube with edge lengths of 4 inches, we need to calculate the space diagonal of the cube. The formula for the diagonal \( d \) of a cube with side length \( a \) is given by:

\[ d = a\sqrt{3} \]

### Step-by-Step Solution:

**Step 1: Identify the side length of the cube.**
- The side length \( a \) of the cube is given as 4 inches.

**Step 2: Substitute the side length into the diagonal formula.**
- Using the formula for the diagonal of the cube:
\[ d = a\sqrt{3} \]
Substituting \( a = 4 \):
\[ d = 4\sqrt{3} \]

**Step 3: Calculate the numerical value of the diagonal.**
- To find the approximate value:
\[ \sqrt{3} \approx 1.732 \]
So,
\[ d \approx 4 \times 1.732 = 6.928 \]

**Step 4: Round the result to two decimal places.**
- The diagonal length can be rounded to:
\[ d \approx 6.93 \text{ inches} \]

### Final Answer:
The longest object that could fit inside the box (the diagonal of the cube) is approximately \( 6.93 \) inches.

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